My sister is in the exact same situation as you. She owns a minivan, boyfriend owns an older (and a bit beat up) Dodge 1500 and combined, they have 5 kids from 9-17 AND a pitbull/mastiff/mutt of a dog (he's a big boy).
IMO, with passengers alone in either vehicle- they were going to be at their maximum carrying capacity long before they added the camper. She figured their best bet was a seasonal site; second best was actually storing the camper at the RV park and then the only time it's towed is from the storage lot on-site to their actual campsite.
My in-laws want to get into RVing and would like their own space vs. staying with us. So as we shopped the RV shows, so did they. My FIL and I talked a lot about dry weights, yellow sticker weights (I literally looked at almost every yellow sticker) and actual loaded weights. First, good for you for looking at the yellow sticker vs. the dry weight. As you found, it's already a fair amount higher than the advertised dry weight.
His question, for me, was that he already had a vehicle and uses it as a traveling trainer for work. He didn't want to upgrade so he asked, "What is the biggest trailer I can tow?" (implying that he wanted to stay within ratings and not just hookup anything and go) Doing the math, his 4Runner only had about 950 pounds of carrying capacity. In order for him to tow the full advertised weight of 7,000 pounds - he had to:
a) lose about 70 pounds
and b) put nothing else in the SUV with him (including my dear mother-in-law!)
The problem is, that 950 pounds is quickly diminished down to what's leftover for tongue weight. Tongue weight is typically 10%-15% of a trailers actual loaded weight.
I wrote some emails to him and published them on my blog:
What can I tow? My FIL's actual example
What can I tow? A general page
You'll likely not be happy with the answer- especially with a family of 5 kids.